Upper Ordovician Kope Formation, Cincinnati Arch

RESEARCH LETTERS RESEARCH LETTERS

High-Resolution Correlation in Apparently Monotonous Rocks: Upper Ordovician Kope Formation, Cincinnati Arch STEVENM. HOLLAND Department of Geology, University of Georgia, Athens, GA 30602-2501

DAVIDL. MEYERand ARNOLDI. MTTTL,ER Department of Geology, University of Cincinnati, Cincinnati, OH 45221-0013

PALAIOS,2000, V. 15, p. 73-80 Short stratigraphic sections in apparently monotonous strata pose several challenges to high-resolution (1 m uncertainty). The discovery of a cluster of articulated trilobites (Hughes and Cooper, 1999) motivated us to devise a method for correlating these smaller outcrops with a high degree of precision into our developing stratigraphic framework for the Kope (Holland et al., 1997). Similar occurrences of well-preserved trilobites and echinoderms are not unusual in the Kope, yet the inability to correlate has hampered the recognition of patterns in the stratigraphic distribution of beds containing unusually well preserved fossils. Because these problems in correlation are not unique to the Kope, the techniques we describe here could apply to other regions of limited exposure and relatively monotonous successions. REGIONAL BACKGROUND

Stratigraphic correlation is one of the most basic of all geologic problems, yet it is frequently one of the least straightforward to solve. All correlation is ultimately based on pattern matching of features thought to be temporally significant. Such features might include overall faunal or lithologic similarity of intervals of strata, or distinctive surfaces such as an ash bed, a sequence boundary, or the first occurrence of a species. In common practice, most correlation is a qualitative exercise lacking a quantifiable measure of the robustness or validity of the correlation. As a result, comparing correlations achieved by different methods is not straightforward and can involve a large degree of personal preference for particular methods. Although several numerical methods of correlation have been developed (Gradstein et al., 1985; Mann and Lane, 1995), in general they have not been widely adopted, with the possible exception of graphic correlation. An additional problem arises when correlating stratigraphically short, isolated outcrops in areas of limited exposure to longer, well-described outcrops. Longer sections are relatively easier to correlate to one another because it

The Kope Formation is exposed throughout northern Kentucky, southwest Ohio, and southeast Indiana. It was deposited over an estimated span of 2-3 million years and comprises most of the C1 depositional sequence of Holland and Patzkowsky (1996) in the Cincinnati area (Fig. 1). The Kope was deposited in an offshore environment on a northward-dipping storm-dominated ramp (Tobin and Pryor, 1981; Jennette and Pryor, 1993). Shale comprises roughly two-thirds of the Kope, with the remainder consisting of very thin to medium beds of calcisiltite, skeletal packstone, and skeletal grainstone, all deposited as storm beds. The Kope exhibits cyclicity at a range of scales (Jennette and Pryor, 1993; Holland et al., 1997). Meter-scale cycles are the smallest of these units and consist of alternating shale-rich intervals and intervals dominated by skeletal packstones and grainstones (Fig. 2). Shale-rich intervals are interpreted as distal storm-bed facies, whereas intervals rich in skeletal packstones and grainstones are interpreted as proximal storm-bed facies (Jennette and Pryor, 1993). Meter-scale cycles show vertical trends in thickness that define larger-scale cycles roughly 20 m thick (Fig. 3). Meter-scale cycles are thicker than average in the lower parts of 20-m cycles and are average to thinner than average near the top. Successive 20-m cycles display an aggradational to slightly progradational stacking pattern, characterized by an upward increase in the proportion of

Copyright C 2000, SEPM(Society for Sedimentary Geology)

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INTRODUCTION

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FIGURE1-Stratigraphy of the Upper Ordovicianon the Cincinnati Arch.Study intervalspans most of the Kope Formationand the basal portionof the FairviewFormationnear Cincinnati.C1 throughC6 sequences refer to third-orderdepositionalsequences recognized by Hollandand Patzkowsky (1996) on the CincinnatiArch, Nashville Dome, and Valleyand Ridge of Tennessee and Virginia.

limestone, which is interpreted to indicate overall upward shallowing within the Kope. The presence of multiple scales of cyclicity has hampered the previous recognition of correlatable lithologic changes. Furthermore, because the limestone-to-shale ratio tends to increase depositionally updip, lithologic changes found in any one area are difficult to follow elsewhere, adding to the sense that vertical lithologic changes are not easily correlated. The study we present here involves the correlation of two outcrops in the Kope of northern Kentucky (Fig. 4). The White Castle section contains the unusual bed of wellpreserved trilobites (Hughes and Cooper, 1999). We correlate this section to a much longer section through the Kope at the K445 composite outcrop (Holland et al., 1997). The K445 section is nearly complete, and ranges from several meters above the basal Kope-Point Pleasant contact to several meters above the contact of the Kope with the overlying Fairview Formation. The White Castle and K445 sections are separated by 9 km.

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ALTERNATEMETHODS OF CORRELATIONIN THE KOPE

FIGURE2-Typical meter-scale cycles of the Kope Formation.Section shown is a portionof the K445 composite outcrop;complete section is in Hollandet al. (1997). Meter-scalecycles consist of a lower shale-rich unit and an upper unit of skeletal packstones and grainstones. Forconsistency among all cycles, cycle boundariesare placed at floodingsurfaces, althoughsome cycles have the structureof sequences (complete with small-scale sequence boundariesand systems tracts) ratherthan parasequences. See Hollandet al. (1997) for a more complete discussion of the anatomyof these meter-scalecycles.

A variety of strategies have been used to correlate within the Kope. Rocks in the Cincinnati area dip gently, usually less than 0.5?, allowing elevation to be used for local correlations. However, even these gentle dips can lead to uncertainties of 5-10 m over distances of a kilometer. As a result, elevation is useful only as an approximate means of correlation. The abundant macrofossils-brachiopods, bryozoans, trilobites, crinoids, and molluscs-have also been used for correlation in the Kope. Most of these have local ranges that are strongly controlled by subtle facies changes, and the abundances of many genera change systematically within the Kope (Fig. 5). For example, the crinoids Cincinnaticrinus and Iocrinus, as well as the thin disc-shaped bryozoan Aspidopora, tend to occur most commonly near

the bases of the 20-m cycles, particularly low within the Kope. These positions are interpreted as relatively deeperwater offshore facies based on storm bed proximality, cycle anatomy, and overall cycle-stacking patterns (Jennette and Pryor, 1993; Holland et al., 1997). Robust bryozoans and the brachiopods Strophomena, Platystrophia, and Rafinesquina occur most commonly near the tops of 20-m cycles and especially near the Kope-Fairview contact. These positions are interpreted as being shallower water, although still deposited within an offshore environment. These relatively shallower and deeper offshore facies in the Kope differ by subtle differences in their limestoneshale ratio that are easily overlooked. Because these taxa are facies controlled, their local ranges within the Kope

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FIGURE3-Fischer plot of meter-scale cycles at the K445 section, displayingsystematicthickeningand thinningtrends.NotethatFischer plot displays only trends in cycle thickness;trianglesshowing thicknesses of individualcycles are not shown. Several 20-m cycles are visible (labeledC1-1, C1-2, etc.). Each 20-m cycle is characterizedby an initialseries of thickerthan average meter-scale cycles followed by several average to thinnerthan average meter-scalecycles. Successive thickeningof cycles is interpretedas upward-deepeningand successive thinningof cycles is interpretedas upward-shallowing.

change in outcrops depositionally updip and downdip. Shallow-water

species tend to have shorter, more frag-

mented stratigraphic local ranges in downdip sections and longer, more continuous local ranges in updip sections. The opposite pattern is true for deep-water species. Thus, correlation purely with fossils is likely to lead to imprecise correlation particularly if followed for more than a few kilometers. Graptolites and conodonts also have been used for cor- FIGURE4-Location of K445 and WhiteCastle outcrops.See appenrelation in the Kope. Although graptolites are common dix for detailed localitydescriptions. and diverse (Bergstrom and Mitchell, 1991; Mitchell and Bergstr6m, 1991), the single zonal boundary recognized within the Kope is insufficient for establishing the numer- of meter-scale cycles changes abruptly. Once a distinctive ous lines of correlation needed to correlate small outcrops contact has been matched, cycles are simply correlated with precision. Conodonts have been used primarily in one to another progressively away from the marker horigraphic correlation and have been effective in correlating zon. Without such a distinctive marker, cycles have been much of the Middle and Upper Ordovician of North Amer- correlated only through qualitative visual matching. Beica (Sweet, 1979; Sweet, 1984). However, the inherent 6-m cause Zeller's (1964) classical experiment in correlation precision of this graphic correlation is too coarse for high- showed how faith in correlation could drive workers to find correlations even in randomly generated stratigraphresolution correlation within the Kope. Some of the more distinctive storm beds within the Kope ic sections, a more quantitative, repeatable, and objective have permitted correlation in limited instances. For ex- method of correlation is preferred. ample, a single bed of gutter casts has been correlated for 43 km, largely along depositional strike (Jennette and CROSS-CORRELATION Pryor, 1993). Similarly, a bed containing abundant DiploTo avoid the problems associated with these alternative craterion, or U-tube trace fossils, has been correlated for over 10 km, also mostly along depositional strike (Tobin, methods, we used the technique of cross-correlation to cor1982). However, such beds are not unique. Gutter casts oc- relate meter-scale cycles (cf. Anderson and Kirkland, cur at a number of stratigraphic levels and Diplocraterion 1966; Dean and Anderson, 1974). As a first step, meteroccurs sporadically throughout the Kope. Correlations us- scale cycles were identified in both sections. Next, the two ing these beds work only if the sections already have been sections were lined up cycle-for-cycle, with the first cycle in the one section correlated to the first in the second secapproximately correlated by other means. Meter-scale cycles also have been used for regional cor- tion, the second cycle with the second cycle, and so on. The relation (Jennette and Pryor, 1993). Most of these cycles thicknesses of pairs of cycles were compared and Pearson's look more or less like any other; hence, it is only where dis- correlation coefficient (r) of cycle thicknesses in the two tinctive features occur, such as abrupt changes in cycle sections was calculated. One section was then shifted by thickness, or where distinctive successions of cycles occur one cycle relative to the other and the process was repeatthat cycles can be matched. In the past, this has been pos- ed. This continued until a correlation coefficient was calsible only near the top and the bottom of the Kope Forma- culated for each possible value of cycle offset. Because the distinctive upper or lower contacts of the tion where the limestone to shale ratio and the thickness

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99%) also can be assigned to this correlation, indicating that the successions of cycle thicknesses in these sections are too similar for this correlation to have arisen by chance. The occurrence of the trilobite lens reported by Hughes and Cooper (1999) can be located within our thicker K445 outcrop to a precision of half a meter within the 60-m thick section. Such correlations of other unusual fossil occurrences in the Kope Formation ultimately may lead to a better understanding of large-scale patterns of beds of unusual preservation and their possible sequence stratigraphic context. DISCUSSION Cross-correlation was used widely in the 1960s and 1970s in early attempts to automate stratigraphic correlation. Its initial successes came with varve correlation, where the thicknesses of successive varves were used to correlate over distances of several hundred kilometers

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FIGURE 8-Final correlation of WhiteCastleandK445sections.Occurrenceof trilobite lens at the WhiteCastlesectionis equivalent to meter-scalecycle16 of the K445section.WhiteCastlesectionspans the C1-1/C1-220-mcycleboundary. Thefewernumberof limestone beds at WhiteCastlereflectsthe less intensivemeasurement of this sectionrelativeto K445.

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best match between the two sections. Provided the secintheWhite tions lack significant gaps, this approach is readily capa7-Presence/absenceof commonmacrofossils FIGURE Castle section. All occurrences are from in situ ledges of limestone, ble of finding correlations. Furthermore, the complicaexcept for "F",whichwere foundin floatand are shown here because tions caused by stratigraphic gaps can be avoided by corthey indicatethe presence of these formsupsection.The trilobitelens relating short sections or short portions of one section with reportedby Hughes and Cooper (1999) is locatedjust below meter2. another much section. In this way, it is unlikely The apparentlylowerdiversityin the WhiteCastle section relativeto that the short longer if chosen section, correctly, will span a gap the K445 section reflectsthe greatersamplingintensityat K445. and lead to an erroneous correlation. Spuriously high correlations can result, however, from random variations in (Anderson and Kirkland, 1966). It also was successfully bed or varve thickness, from cyclic variations in thickness, applied to the correlation of turbidite successions, again or from net trends in thickness. Other geologic evidence based on the thicknesses of successive beds (Dean and An- must be used to eliminate these spurious correlations. Cross-correlation techniques were later extended to othderson, 1967). Both of these studies used the Sliding Correlation Coefficient (Dean and Anderson, 1974), in which er types of data, particularly electric log data collected bed or laminae thickness is the dependent variable and from wells. Some property, such as resistivity or gamma bed or lamina number is the independent variable. The response (the dependent variable) was measured as a thicknesses of the varves or beds in the two sections pro- function of depth in the well (the independent variable). gressively are correlated to one another for different val- By using a Moving Correlation Coefficient (Dean and Anues of offset. The peak value in correlation is the statistical derson, 1974) the dependent variables of both sections are

HIGH-RESOLUTION CORRELATION HIGH-RESOLUTION CORRELATION correlated, and the sections are progressively offset by some constant value of rock thickness. This is repeated for all possible values of offset, and the offset with the highest correlation coefficient is considered the best statistical match between the sections. This broader application of cross-correlation raised a number of additional complications (Robinson, 1978; Southam and Hay, 1978; Mann, 1979; Rock, 1988). First, both sections must be measured and sampled in equal increments of rock thickness for the two series to be mathematically comparable. Second, this basic approach is unable to accommodate the inevitable changes in sedimentation rate through time and between the two sections. These changes in rate must be corrected for by routines that stretch or shrink sections to find the best correlation. The resulting increased complexity of these methods apparently did not result in significantly improved correlations and their results were described as discouraging and disappointing (Mann, 1979). Davis (1986) stated that "these efforts have met with a notable lack of success, except in special circumstances," such as varve correlation. Ultimately, cross-correlation for stratigraphic correlation fell into disuse. Correlations of sedimentary cycles can be considered one of Davis' (1986) special circumstances, because like varves, cycles are packages of rock bounded by correlative surfaces. Cycle thickness is recorded as a function of cycle number, not stratigraphic position. Because changes in sedimentation rate and cycle period control cycle thickness, they allow the sections to be correlated instead of being obstacles to the method. Ideally, one section should contain more cycles than the other and the short section should correlate entirely within the interval of the longer section. Identifying distinctive stratigraphic markers at the top and base of the section, such as prominent sequence stratigraphic surfaces, event beds, or biostratigraphic datums, can achieve this. In addition, the sections should lack significant unconformities. At a minimum, the location of such unconformities should be known so that erroneous cross-correlations can be detected. Finally, sections must be of sufficient length-at least several cycles long-for cross-correlation to produce meaningful results. Cross-correlation of cycles cannot be used in cases where the locations of the outcrops experienced peaks in sediment supply at different points in time. For example, cross-correlation could erroneously correlate two sections widely spaced along depositional dip by matching the upward thickening of cycles within the lowstand systems tract of the downdip outcrop with that of the highstand systems tract of the updip outcrop. Likewise, cross-correlation would incorrectly correlate cycles in a series of clinoforms because it would tend to match the thickest cycles in each section. In reality, these thickest cycles in each outcrop would be successively younger towards the center of the basin. Because of these problems, cross-correlation will work best for sections that are closely spaced geographically or from sections on flat-topped platforms that experience nearly synchronous changes in accommodation and sediment supply. Where conditions permit its use, cross-correlation can provide a start to high-precision correlations, particularly in rocks that lack distinctive event beds or cycles that are readily distinguished from other cycles; in other words, apparently monotonous successions. In cases like these,

79 cross-correlation may represent the only way that short sections in areas of limited exposure can be correlated to long sections. The method of cross-correlation will work only to the extent that subsidence rate and long-term sedimentation rate are relatively consistent between outcrops. Over short time scales of several dozen cycles and over short distances dominated by flexural rather than fault-controlled subsidence, these conditions are likely to be true. If longer period cycles or trends are present in the section that give rise to multiple possible correlations, other geologic criteria, including the presence of fossils, can be used to choose among the correlations. In this way, crosscorrelation does not fully automate the process of correlation, but is used to narrow the range of potential correlations that can be selected by other geologic data. In addition, cross-correlation permits the calculation of confidence levels on the correlation, thereby providing a standard for the robustness of the correlation. The method presented here is attractive because it can be applied quickly once the longer sections are described. Although bed-by-bed measurement and faunal description of the K445 section took place over several weeks (largely because every bed thicker than 5 mm was described), the White Castle section was measured and described in a little over an hour and a half. No attempt was made at White Castle to measure every bed or thoroughly describe the fauna. Major limestone beds defining cycle boundaries were measured and a quick tally of the common fossils was made. Because not all sections have to be described to the detail of the thicker primary outcrops, correlation of numerous small outcrops can proceed rapidly. CONCLUSIONS (1) The combination of cross-correlation of meter-scale cycles, supplemented by patterns of fossil occurrence, can permit high-resolution correlations in successions previously considered to be monotonous. Even facies fossils can be sufficient for distinguishing among potential correlations suggested by cross-correlation. This approach has particular promise in areas lacking distinctive event beds or other marker horizons and in areas of limited outcrop where numerous small sections need to be correlated to a few more widely spaced, thicker, and better described outcrops. Cross-correlation also allows a quantified measure of the statistical confidence of the correlation, unlike traditional methods. Finally, the method described here can be employed rapidly once the initial detailed descriptions of the primary localities have been made. (2) Although cross-correlation was used widely in the 1960s and 1970s as a means of correlation, but then largely abandoned, it has potential use in correlating meterscale cycles over short distances where significant unconformities are absent. Such use is much closer to the original and highly successful application of cross-correlation to varves than the more disappointing results obtained when the method was later applied to geophysical well logs. ACKNOWLEDGMENTS We thank Nigel Hughes for generously sharing his work on the White Castle locality and for commenting on a draft

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of this manuscript. We also thank B.F. Dattilo for reduction of the K445 faunal data used in Figure 5 as well as the two anonymous PALAIOSreviewers for their helpful comments. This research was supported by NSF Grants EAR9204445 to S.M. Holland and EAR-9204916 to A.I. Miller and D.L. Meyer. Software used in this study for automatic cross-correlation of cycles in two stratigraphic sections and for the calculation of significant values of correlation coefficient is available at http://www.uga.edu/-strata or directly from S.M. Holland. REFERENCES

MITCHELL,C.E., and BERGSTROM, S.M., 1991, New graptolite and lithostratigraphic evidence from the Cincinnati region, U.S.A., for the definition and correlation of the base of the Cincinnati Series (Upper Ordovician): Geological Survey of Canada Paper, v. 90-9, p. 59-75. ROBINSON, J.E., 1978, Pitfalls in automatic lithostratigraphic correlation: Computers & Geosciences, v. 4, p. 273-275. ROCK,N.M.S., 1988, Numerical Geology:Springer-Verlag,Berlin, 427 p. SOUTHAM,J.R., and HAY, W.W., 1978, Correlation of stratigraphic sections by continuous variables: Computers & Geosciences, v. 4, p. 257-260. SWEET,W.C., 1979, Conodonts and conodont biostratigraphy of postTyrone Ordovician rocks of the Cincinnati region: United States Geological Survey Professional Paper 1066-G, p. 1-26. SWEET,W.C., 1984, Graphic correlation of upper Middle and Upper Ordovician rocks, North American Midcontinent Province, U.S.A.: in BRUTON,D.L., ed., Aspects of the Ordovician System: University of Oslo, Oslo, p. 23-35. TOBIN, R.C., 1982, A model for cyclic deposition in the Cincinnatian Series of southwestern Ohio, northern Kentucky and southeastern Indiana: Unpublished Ph.D. Dissertation, University of Cincinnati, 483 p. TOBIN,R.C., and PRYOR,W.A., 1981, Sedimentological interpretation of an Upper Ordovician carbonate-shale vertical sequence in northern Kentucky: in ROBERTS,T.G., ed., Geological Society of America Cincinnati '81 Field Trip Guidebooks. Volume I: Stratigraphy, sedimentology: American Geological Institute, Falls Church, p. 49-57. ZELLER,E.J., 1964, Cycles and psychology: Geological Survey of Kansas Bulletin, v. 169, p. 631-636.

ANDERSON, R.Y., and KIRKLAND, D.W., 1966, Intrabasin varve correlation: Geological Society of America Bulletin, v. 77, p. 241-256. BERGSTROM, S.M., and MITCHELL, C.E., 1991, Trans-pacific graptolite faunal relations: The biostratigraphic position of the base of the Cincinnatian Series (Upper Ordovician) in the standard Australian graptolite zone succession: Journal of Paleontology, v. 64, p. 992-997. DAVIS,J.C., 1986, Statistics and Data Analysis in Geology: John Wiley & Sons, New York, 646 p. DEAN,W.E., JR., and ANDERSON, R.Y., 1967, Correlation of turbidite strata in the Pennsylvanian Haymond Formation, Marathon Region, Texas: Journal of Geology, v. 75, p. 59-75. DEAN,W.E., JR., and ANDERSON,R.Y., 1974, Application of some correlation coefficient techniques to time-series analysis: Mathematical Geology, v. 6, p. 363-372. GRADSTEIN, F.M., AGTERBERG, F.P., BROWER, J.C., and SCHWARZACHACCEPTED JULY 21,1999 ER, W.S., 1985, Quantitative Stratigraphy: Kluwer, Dordrecht, 598 p. HOLLAND, S.M., and PATZKOWSKY, M.E., 1996, Sequence stratigraphy APPENDIX and long-term lithologic change in the Middle and Upper Ordovician of the eastern United States: in WITZKE,B.J., LUDVIGSEN, Locality descriptions G.A., and DAY,J.E., eds., Paleozoic sequence stratigraphy: Views from the North American craton: Geological Society of America White Castle. Roadcut on hillside, immediately east and behind White Castle processing plant, located on Kentucky State Route 17, Special Paper 306, p. 117-130. HOLLAND,S.M., MILLER,A.I., DATTILO, B.F., MEYER,D.L., and DIEK- 1.5 kilometers south of 1-275 overpass. Covington, KY-OH 7 1/2' MEYER, S.L., 1997, Cycle anatomy and variability in the stormquadrangle. 39? 00' 30" N, 84? 31' 47" W. dominated type Cincinnatian (Upper Ordovician): Coming to grips K445 Composite. Composite outcrop consists of four sections: K445, with cycle delineation and genesis: Journal of Geology, v. 105, p. CON1, CON2, and CON3. K445: Roadcut on both sides of Kentucky 135-152. State Route 445, 0.2 km west of intersection with Kentucky State Route 8, immediately northwest of the 1-275 bridge over the Ohio RivHUGHES,N.C., and COOPER,D.L., 1999, Paleobiologic and taphonomic aspects of the "granulosa" trilobite assemblage, Kope Formation er near Old Coney Amusement Park. Newport, KY-OH 7 1/2' quad(Upper Ordovician, Cincinnati region): Journal of Paleontology, v. rangle. 39? 03' 22" N, 84? 26' 10"W. CON1: First roadcut on northwest side of westbound 1-275, 0.5 km southwest of intersection of I-275 and 73, p.306-319. JENNETTE,D.C., and PRYOR,W.A., 1993, Cyclic alternation of proxi- the Kentucky bank of Ohio River near Old Coney Amusement Park. mal and distal storm facies: Kope and Fairview Formations (UpNewport, KY-OH 7 1/2' quadrangle. 39? 03' 15" N, 84? 26' 20" W. CON2: Second roadcut on northwest side of westbound 1-275, 0.6 km per Ordovician), Ohio and Kentucky: Journal of Sedimentary Pesouthwest of intersection of I-275 and the Kentucky bank of Ohio Rivtrology, v. 63, p. 183-203. er near Old Coney Amusement Park. Newport, KY-OH 7 1/2' quadMANN,C.J., 1979, Obstacles to quantitative lithostratigraphic correlation: in GILL,D., and MERRIAM,D.F., eds., Geomathematical rangle. 39? 03' 13" N, 84? 26' 24" W. CON3: Third roadcut on northand Petrophysical Studies in Sedimentology: Pergamon Press, west side of westbound 1-275, 0.8 km southwest of intersection of I275 and the Kentucky bank of Ohio River near Old Coney AmuseOxford, p. 149-165. ment Park. Newport, KY-OH 7 1/2' quadrangle. 39? 03' 10"N, 84? 26' MANN,K.O., and LANE,H.R., eds., 1995, Graphic Correlation: SEPM 30" W. Special Publication No. 53, 263 p.